Algebra 2 midterm

Directions:  Use what you have learned in this course to answer the following questions. Justify your responses completely. Each question is worth 5 points. 
1. Solve for n:  –6(n – 8) = 4(12 – 5n) + 14n.
2. For f(x) = 2|x+3| – 5, name the type of function and describe each of the three transformations from the parent function f(x) = |x|.
3. Determine whether f(x) = –5 – 10x + 6 has a maximum or a minimum value. Find that value and explain how you know.
4. The median weekly earnings for American workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999.
5. Find the roots of the parabola given by the following equation. 
2×2+ 5x – 9 = 2x
6. Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros.
7. GEOMETRY Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions of a rectangle that has an area 144 square inches, given that the length is 10 inches longer than its width. 
DIMENSIONS:
Length: Width:
8.  The amount f(t) of a certain medicine, in milligrams, in a patient’s bloodstream t minutes after being taken is given by f(t) = . 
Find the amount of medicine in the blood after 20 minutes.
9.  Graph f(x) = x2 + 2x – 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry.

Image result for x y axis
10. Determine whether the relation shown is a function. Explain how you know.

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11.  Solve the inequality and graph the solution on a number line. 
–3(5y – 4) ≥ 17
12.  Assume that the wooden triangle shown is a right triangle.
​​
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram. 
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
13. Use long division or synthetic division to find the quotient of .
14. Simplify (9 + 8 – 6)(4 – 5).
15. Find the inverse of h(x) = .
16.  If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
17. Graph the function y = – 2. Then state the domain and range of the function. 
Domain:
Range: 
18. If f(x) = 3×2 – 2 and g(x) = 4x + 2, what is the value of f + g 2 ?
The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
19.  Let w represent the price of one sweatshirt, t represent the price of one T-shirt, and h represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.
20. Solve the system. Find the cost of each item.

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